Eisinger J, Halperin B I
Biophys J. 1986 Sep;50(3):513-21. doi: 10.1016/S0006-3495(86)83489-0.
There exist many examples of membrane components (e.g. receptors) accumulating in special domains of cell membranes. We analyze how certain variations in lateral diffusibility and solubility of the membrane would increase the efficiency of transport to these regions. A theorem is derived to show that the mean-time-of capture, tc, for particles diffusing to a trap from an annular region surrounding it, is intermediate to the tc values that correspond to the minimum and maximum diffusion coefficients that obtain in this region. An analytical solution for tc as a function of the gradient of diffusivity surrounding a trap is derived for circular geometry. Since local diffusion coefficients can be increased dramatically by reducing the concentration of intra-membrane particles and/or allowing them to form aggregates, such mechanisms could greatly enhance the diffusion-limited transport of particular membrane components to a trap (e.g. coated pit). If the trap is surrounded by an annular region in which the probe particles' partition function is increased, say, by the local segregation of certain phospholipids, tc is shown to vary inversely with the logarithm of the relative partition function. We provide some conjectural examples to illustrate the magnitude of the effects which heterogeneities in diffusibility and solubility may have in biological membranes.
存在许多细胞膜成分（如受体）在细胞膜特定区域积累的例子。我们分析了膜的横向扩散率和溶解度的某些变化如何提高向这些区域运输的效率。推导了一个定理，表明从围绕陷阱的环形区域扩散到陷阱的粒子的平均捕获时间(t_c)，介于该区域获得的最小和最大扩散系数对应的(t_c)值之间。针对圆形几何形状，推导了(t_c)作为陷阱周围扩散率梯度函数的解析解。由于通过降低膜内粒子浓度和/或允许它们形成聚集体可显著提高局部扩散系数，因此这种机制可极大增强特定膜成分向陷阱（如被膜小窝）的扩散限制运输。如果陷阱被一个环形区域包围，其中探针粒子的分配函数增加，例如通过某些磷脂的局部分离，(t_c)显示与相对分配函数的对数成反比。我们提供了一些推测性例子来说明扩散率和溶解度的异质性在生物膜中可能产生的效应大小。
